Stability analysis of an SVLI epidemic model

Abstract

Immunization with the Bacillus Calmette-Guérin vaccine is currently used in many parts of the world as a means of preventing tuberculosis even though it remains a highly controversial method of preventing tuberculosis disease. We develop a deterministic mathematical model for the transmission dynamics of tuberculosis to monitor the effect of BCG vaccine, which may wane over time and which is not 100 % effective, on tuberculosis epidemiology. The analysis of the presented model has provided conditions to guarantee the eradication of the disease in terms of three major parameters incorporated into the model; the vaccination coverage level, the waning rate and the efficacy of the vaccine. © 2010 Springer-Verlag Berlin Heidelberg.